Wow that's a big trip. I did just over 2,500 in 10 day through Europe but only as far down as Mont Blanc. How many days are you planning for this?
I'd say with a trip this big I'd make sure the car is full of all fluids and maybe take a couple of litres of oil with you? Tyres, pads and so on are in good condition.
Gota say this could cost a fair bit on fuel too, I'm sure I spent near to £500 for the ten days.
Keep us posted, this will be epic